perf: in-place Cholesky buffer + copy-free numba solves for fnnls_cholesky

[Jammy2211]

Closes #452.

What

The positive-only inversion solve (fnnls_cholesky) dominates the numba CPU Delaunay likelihood (~74% of a euclid eval on the production campaign fiducial — PyAutoLabs/autolens_profiling#151). The cost was implementation, not linear algebra: ~150 Bro–Jong active-set iterations, each rebuilding the ~1300² Cholesky factor via np.insert/np.delete (two O(n²) copies per change), plus scipy solve_triangular/cho_solve re-copying and finite-scanning the factor on every call.

Three changes, same mathematics:

• In-place factor buffer — the factor lives in the top-left k×k corner of one preallocated buffer, grown by cholinsertlast_inplace and shrunk by choldeleteindexes_inplace; the existing numba Givens up/down-date kernels are unchanged (verified bitwise-stable on strided views). The out-of-place cholinsertlast/choldeleteindexes remain for reference and tests.
• Copy-free numba solves — _solve_upper_transposed_buffer (row-oriented forward substitution) and _cho_solve_buffer read the buffer's upper triangle directly, replacing the per-iteration scipy calls. This half is essential: with scipy still in the loop, its per-call copy of the strided view cancels the buffer's win (measured: no speedup with the buffer alone).
• Numba shift kernel for deletes (_choldelete_shift_buffer) — numpy's overlapping slice assignments buffer the source region, re-introducing per-delete temp allocations; the kernel closes the deleted row/column gap with plain loops (bitwise-identical value movement).

Results (4-core cloud container, Delaunay Hilbert-1250 campaign fiducial)

• Real euclid 1310-param system: solve 3.29 s → 1.16 s (2.83×), identical active set, solutions agree to ~1e-9 absolute.
• Pinned autolens_profiling delaunay_numba cells (feat: numba CPU sparse-operator likelihood profiling (runtime, breakdown, multiprocessing scaling) autolens_profiling#152, rtol 1e-6) pass: euclid eval 4.92 → 2.34 s (2.10× end-to-end); hst 3.95 → 3.43 s.

Numerical equivalence

Results are not bitwise identical to the old path: LAPACK/our kernels pick layout-dependent but equally valid evaluation orders, and the old implementation already mixed memory layouts between its own iterations (scipy.linalg.cholesky returns F-order, np.insert/np.delete return C-order). Equivalence is enforced in the new test_autoarray/util/test_cholesky_inplace.py: cross-implementation agreement at 1e-13, exact factor-property checks (U′U = active submatrix), scipy.optimize.nnls cross-checks, and warm-start = cold-start. The degeneracy guard (_pivot_from_schur) and the producer-side non-finite check in fnnls_cholesky are unchanged.

Testing

• test_autoarray/: 1026 passed, 51 skipped; the only failures are 3 pynufft transformer tests that fail identically on stock main in this environment (pre-existing).
• New: test_autoarray/util/test_cholesky_inplace.py (18 tests).

Downstream

No public-API change — fnnls_cholesky(ZTZ, ZTx, P_initial) signature and caller (inversion_util.reconstruction_positive_only_from) are untouched. fix_constraint_cholesky's (module-internal) signature changed to thread the buffer. Likelihood values shift at the ~1e-9 relative level, within the established solver bistability tolerance (profiling pins use rtol 1e-6).

Block-pivoting / block-insertion phase-2 variants were prototyped and rejected (cycling / masked non-convergence on this system's near-degenerate columns) — findings in #452.

🤖 Generated with Claude Code

https://claude.ai/code/session_01Vcc7MUBMnNU6n8qqS9ioVZ